The Peak Over Threshold (POT) method, described in details by [1]},
has been used in many fields to identify extremal events such as loads,
wave heights, floods, wind velocities, etc. This method provides a
model for independent exceedances over a high threshold.
According the
Pickands-Balkema-de Haan theorem [2]}, [3]}
for a threshold \(u\)  sufficiently high, the unnormalized conditional tail distribution of a random variable \(Y\)  can be approximated as
\(\Pr (Y-u\le y|Y>u)\approx H_{\xi }(y/\psi _u),\qquad \text{for}\, y\ge 0\quad \text{and}\quad \psi _u >0\) 
